Alternative model structure with simplistic noise model to identify linear time invariant systems subjected to non-stationary disturbances

Non-stationary disturbances are of common occurrence in chemical process industry. These cannot be modeled using constant parameterized models and hence pose a difficult problem in the identification of true process and disturbance dynamics. A simple system identification technique to identify the linear processes affected by non-stationary disturbances is proposed in this work. This uses a time varying bias term, a representative of the additive non-stationary external disturbance entering the process, in addition to the output predictions in an ARMAX or OE model framework. Decoupled loss function and covariance update with different forgetting factors for linear time invariant input-output dynamics part and time varying part (bias term) of the model ensures the unbiased estimation of true process dynamics along with disturbance dynamics. Practical issues such as time delay estimation, model order selection are discussed. Extensions for time varying processes and MIMO processes are also proposed. Validation is performed using various simulation studies.